Paper 2021/1034
Optimal encodings to elliptic curves of $j$-invariants $0$, $1728$
Abstract
This article provides new constant-time encodings $\mathbb{F}_{\!q}^* \to E(\mathbb{F}_{\!q})$ to ordinary elliptic $\mathbb{F}_{\!q}$-curves $E$ of $j$-invariants $0$, $1728$ having a small prime divisor of the Frobenius trace. Therefore all curves of $j = 1728$ are covered. This circumstance is also true for the Barreto--Naehrig curves BN512, BN638 from the international cryptographic standards ISO/IEC 15946-5, TCG Algorithm Registry, and FIDO ECDAA Algorithm. Many $j = 1728$ curves as well as BN512, BN638 are not appropriate for the most efficient prior encodings. So, in fact, only universal SW (Shallue--van de Woestijne) one was previously applicable to them. However this encoding (in contrast to the new ones) cannot be computed at the cost of one exponentiation in the field $\mathbb{F}_{\!q}$.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Preprint.
- Keywords
- encodings to (hyper)elliptic curves isogenies $j$-invariants $0$ and $1728$ optimal covers Weil pairing
- Contact author(s)
- dimitri koshelev @ gmail com
- History
- 2022-11-16: last of 4 revisions
- 2021-08-16: received
- See all versions
- Short URL
- https://ia.cr/2021/1034
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1034,
author = {Dmitrii Koshelev},
title = {Optimal encodings to elliptic curves of $j$-invariants $0$, $1728$},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1034},
year = {2021},
url = {https://eprint.iacr.org/2021/1034}
}
